Sift the flour and salt into a large bowl and cut in the butter and shortening until the mixture resembles coarse meal.
Add the water, toss the mixture, and form it into a ball.
Halve the dough, wrap in wax paper, and chill for 30 minutes.
Sprinkle the mincemeat with the rum, sherry or cognac, to taste and let it stand for 15 minutes.
Roll out one half of the dough to 1/8 inch thickness and cut out rounds with a 4 1/2 inch cutter.
Fit each round into a 12 cup muffin tin.
Divide the mincemeat among the cups and brush the edges of the dough with the egg glaze.
Roll out the remaining dough, cut out rounds with a 3 1/2 inch cutter, and fit each round over the mincemeat, gently pressing it down over the filling and crimping the top crust to the bottom.In a blender blend the sugar until it is fine.
Brush the top of the dough with the glaze and bake the pies on a baking sheet in the lower third of oven at 375° F for 15 minutes.
Brush with the glaze again and bake for 15 minutes more.
Once again brush with the glaze, and transfer to the middle of the oven.
Continue to bake the pies for 10 to 15 minutes more or until they are golden brown.
Transfer the muffin tins to racks, sprinkle with the sugar, and let cool completely.
With the tip of a knife, loosen the pies from the tins; lift out and transfer to airtight containers.
The pies will keep, tightly covered in a cool dry place, for 1 week.